Solve (18-10)² + 3³: Combined Square and Cube Number Problem

Order of Operations with Square and Cube Numbers

Solve the following question:

(1810)2+33= (18-10)^2+3^3=

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:07 Let's solve this math problem together!
00:10 First, we calculate inside the parentheses. Always start there.
00:23 Next, let's handle the powers. Remember, exponents come after parentheses.
00:29 Now, let's add the numbers and solve the equation.
00:33 Great job! You've found the solution.

Step-by-step written solution

Follow each step carefully to understand the complete solution
1

Understand the problem

Solve the following question:

(1810)2+33= (18-10)^2+3^3=

2

Step-by-step solution

To solve the expression (1810)2+33 (18-10)^2+3^3 , we need to follow the order of operations, often remembered by the acronym PEMDAS (Parentheses, Exponents, Multiplication and Division, Addition and Subtraction).

  • Step 1: Parentheses
    First, solve the expression inside the parentheses: 1810 18-10 .
    1810=8 18-10 = 8

  • Step 2: Exponents
    Next, apply the exponents to the numbers:
    (8)2 (8)^2 and 33 3^3 .
    82=64 8^2 = 64
    33=27 3^3 = 27

  • Step 3: Addition
    Finally, add the results of the exponentiations:
    64+27 64 + 27
    64+27=91 64 + 27 = 91

Thus, the final answer is 91 91 .

3

Final Answer

91

Key Points to Remember

Essential concepts to master this topic
  • PEMDAS Rule: Parentheses first, then exponents, then addition/subtraction
  • Technique: Calculate 82=64 8^2 = 64 and 33=27 3^3 = 27 separately first
  • Check: Verify (1810)2+33=64+27=91 (18-10)^2 + 3^3 = 64 + 27 = 91

Common Mistakes

Avoid these frequent errors
  • Adding before calculating exponents
    Don't add 8 + 3 = 11 then square it = 121 + 27 = 148! This ignores the order of operations and produces completely wrong results. Always calculate all exponents before doing addition or subtraction.

Practice Quiz

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\( 20\div(4+1)-3= \)

FAQ

Everything you need to know about this question

Why can't I just work from left to right?

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Mathematics has a specific order of operations (PEMDAS) that ensures everyone gets the same answer. Working left to right ignores exponents and gives wrong results!

What's the difference between 8² and 3³?

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82 8^2 means 8 × 8 = 64 (square), while 33 3^3 means 3 × 3 × 3 = 27 (cube). The small number tells you how many times to multiply!

Do I need to show every step?

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Yes! Always show: (1) Parentheses calculation, (2) Each exponent separately, (3) Final addition. This helps you avoid mistakes and shows your thinking clearly.

What if I forget PEMDAS during a test?

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Remember: Please Excuse My Dear Aunt Sally! Or think: parentheses are like containers that must be opened first, then exponents are the most powerful operations.

Can I use a calculator for the exponents?

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Yes, but make sure you know how! For 33 3^3 , you might press 3, then the exponent button (^), then 3. Practice with simple examples first.

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